sLTN: Structural Logic Tensor Networks

2026-08-11

AI Summary

This work addresses the limitation of classical Logic Tensor Networks (LTNs) in explicitly modeling structured data such as temporal sequences or graphs. It proposes Structured Logic Tensor Networks (SLTN), which for the first time incorporate structural dimensions—such as time steps, sequence positions, or graph nodes—as first-class elements within a neurosymbolic framework. This enables direct expression of structure-aware quantification and constraints at the logical level, while supporting differentiable inference through tensor operations. Implemented in PyTorch, the framework employs a declarative signature, formula parsing, and fuzzy logic semantics. Empirical evaluation on representative temporal and sequential reasoning tasks demonstrates its effectiveness, and the accompanying open-source sltn library aims to advance research in structured neurosymbolic reasoning.

Abstract

Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.

Problem

• Logic Tensor Networks
• structural organization
• temporal order
• sequential position
• graph connectivity

Innovation

• Structural Logic Tensor Networks
• neurosymbolic AI
• tensor semantics
• structured data reasoning
• differentiable logic